role of mesoscale eddies in cross-frontal transport of heat ......ekman layer, the southward eddy...

Role of Mesoscale Eddies in Cross-Frontal Transport of Heat andBiogeochemical Tracers in the Southern Ocean

CAROLINA O. DUFOUR,* STEPHEN M. GRIFFIES,1 GREGORY F. DE SOUZA,*,& IVY FRENGER,*ADELE K. MORRISON,* JAIME B. PALTER,#,** JORGE L. SARMIENTO,* ERIC D. GALBRAITH,@

JOHN P. DUNNE,1 WHIT G. ANDERSON,1 AND RICHARD D. SLATER*

*Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey1NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

#Department of Atmospheric and Oceanic Science, McGill University, Montreal, Quebec, Canada@Department of Earth and Planetary Science, McGill University, Montreal, Quebec, Canada

(Manuscript received 26 November 2014, in final form 24 August 2015)

ABSTRACT

This study examines the role of processes transporting tracers across the Polar Front (PF) in the depth interval

between the surface and major topographic sills, which this study refers to as the ‘‘PF core.’’ A preindustrial

control simulation of an eddying climate model coupled to a biogeochemical model [GFDL Climate Model,

version 2.6 (CM2.6)– simplified version of theBiogeochemistrywithLight IronNutrients andGas (miniBLING)

0.18 oceanmodel] is used to investigate the transport of heat, carbon, oxygen, and phosphate across the PF core,with a particular focus on the role of mesoscale eddies. The authors find that the total transport across the PF

core results from a ubiquitous Ekman transport that drives the upwelled tracers to the north and a localized

opposing eddy transport that induces tracer leakages to the south at major topographic obstacles. In the Ekman

layer, the southward eddy transport only partially compensates the northwardEkman transport, while below the

Ekman layer, the southward eddy transport dominates the total transport but remains much smaller in mag-

nitude than the near-surface northward transport. Most of the southward branch of the total transport is

achieved below the PF core, mainly through geostrophic currents. This study finds that the eddy-diffusive

transport reinforces the southward eddy-advective transport for carbon and heat, and opposes it for oxygen and

phosphate. Eddy-advective transport is likely to be the leading-order component of eddy-induced transport for

all four tracers. However, eddy-diffusive transport may provide a significant contribution to the southward eddy

heat transport due to strong along-isopycnal temperature gradients.

1. Introduction

The Southern Ocean (south of 308S) is a key regionfor themeridional transport of heat and biogeochemical

tracers and one of the fewplaces in the global oceanwhere

ancient deep waters are exposed to the atmosphere

(Marshall and Speer 2012; Talley 2013; Morrison et al.

2015).Within the latitudes of the Antarctic Circumpolar

Current (ACC), vigorous wind-driven upwelling brings

old waters, poor in oxygen and rich in natural carbon and

nutrients, to the surface. Once upwelled, much of the

water heads northward in the surface layer, driven by an

intense Ekman transport. At the northern boundary of

the ACC, it reaches the formation sites of Antarctic

Intermediate Water (AAIW) and Subantarctic Mode

Water (SAMW). AAIW and SAMW are then sub-

ducted into the ocean interior together with heat, car-

bon, oxygen, and nutrients. Upwelling and subduction

are thus important mechanisms for ventilation of the

deep ocean (DeVries and Primeau 2011; Khatiwala et al.

2012) and for long-term sequestration of physical and

biogeochemical anomalies, as well as for the export of

nutrients to low latitudes (Sarmiento et al. 2004; Palter

et al. 2010).

& Current affiliation: ETHZurich, Institute ofGeochemistry and

Petrology, Zurich, Switzerland.

** Current affiliation: Graduate School of Oceanography, Uni-

versity of Rhode Island, Narragansett, Rhode Island.

Corresponding author address: Carolina O. Dufour, Program in

Atmospheric and Oceanic Sciences, 300 Forrestal Road, Sayre

Hall, Princeton, NJ 08544.

E-mail: [email protected]

Denotes Open Access content.

DECEMBER 2015 DUFOUR ET AL . 3057

DOI: 10.1175/JPO-D-14-0240.1

� 2015 American Meteorological Society

mailto:[email protected]

However, meridional transport in the Southern

Ocean requires crossing multiple intense jets that form

the ACC fronts and act as natural barriers to tracer

transport. Both observational and experimental studies

have demonstrated that mixing across the core of jets is

strongly inhibited due to the speed of the jet being

higher than the propagation speed of eddies, hence

reducing the time during which eddies can stir tracers

(e.g., Bower et al. 1985; Lozier et al. 1997; Sommeria

et al. 1989; Ferrari and Nikurashin 2010). Nonetheless,

strong perturbations, such as rings detaching from the

front, might provide a way for tracers to cross the jet

cores (Samelson 1992; Wiggins 2005). Enhanced cross-

frontal transport occurs primarily in two regions of the

jets: in the Ekman layer and at the critical levels (also

called steering levels). In the Ekman layer (the upper

;100–200m), studies have reported vigorous cross-frontal transport driven by northward Ekman flow

(Rintoul and England 2002; Ito et al. 2010; Palter et al.

2013; Holte et al. 2013). At critical levels, observations,

theory, and models have diagnosed high effective eddy

diffusivities, attributed to the rate at which mesoscale

eddies stir properties on interior isopycnal surfaces

(Smith and Marshall 2009; Abernathey et al. 2010;

Naveira Garabato et al. 2011). These critical levels

follow the outer boundary of the jet core, from the

edges of the jet to the deepest extension of its core,

which typically lies between 1 and 1.5 km, and corre-

spond to the depths where eddies drift at the same

speed as the jet. Hence, mesoscale eddies might well be

another important driver of the cross-frontal tracer

transport.

Mesoscale eddies are known to transport tracers

through two processes: Eddy-advective transport [also

known as the Gent andMcWilliams (1990) effect] results

from the eddies extracting the potential energy imparted

by winds from the mean flow, inducing a flattening of

isopycnal surfaces, and hence opposing the wind-driven

circulation (i.e., Ekman and geostrophic transport; Gent

and McWilliams 1990; Gent et al. 1995). Eddy-diffusive

transport (also known as isopycnal or neutral diffusion)

results from the eddies stirring tracers along interior

isopycnal surfaces, inducing a downgradient tracer flux

(Solomon 1971; Redi 1982). Eddy-advective and eddy-

diffusive transports can either reinforce or oppose each

other, and their relative importance varies as a function of

the time-scale considered and the distribution and mixed

layer residence time of the biogeochemical tracer they act

upon (Lee et al. 1997).

As a region of strong baroclinic instability, the

Southern Ocean spawns a rich mesoscale eddy field.

Where the ACC is unbounded, that is generally above

;2 km, there are no net along-stream pressure gradients

to support cross-stream geostrophic currents. Hence,

cross-frontal tracer transport should mainly result from

the competition between Ekman transport and eddy

transport (advective and diffusive contributions), with

eddies as the main conveyer of tracer transport below the

Ekman layer. Marshall and Speer (2012) thus argue that

mesoscale eddies play a leading role in driving the up-

welling of deep waters to the Antarctic Divergence

(;608S). Additionally, enhanced eddy activity has beenreported in specific locations along the path of the ACC,

inducing intense cross-frontal transport (e.g., Naveira

Garabato et al. 2011; Thompson and Sallée 2012). Wherethe fronts flow around major topographic obstacles,

hence developing large-scale meanders, departures from

parallel flow conditions break the prevalent regimewhere

cross-frontal transport is inhibited (Naveira Garabato

et al. 2011). Such ‘‘hotspots’’ of transport, or ‘‘leaky jet’’

segments, show enhanced effective eddy diffusivity, thus

allowing more tracer transport across the fronts (Naveira

Garabato et al. 2011; Thompson and Sallée 2012; Salléeet al. 2008b).

Despite its importance, the net effect of the mesoscale

eddy activity on the cross-frontal transport of climate

relevant tracers such as heat, carbon, oxygen, and nu-

trients has not yet been elucidated. The investigation of

processes driving the cross-frontal transport of tracers,

in particular mesoscale eddies, remains a challenge due

to the scarcity of observations. On the modeling side,

however, this investigation has recently become feasible

due to the advent of eddying climate models coupled to

biogeochemical components.

In this study, we address the role of mesoscale eddies

in the transport of heat and biogeochemical tracers

across the fronts of the ACC.We focus on regions where

(i) jets are strong, hence providing a barrier to tracer

transport, and (ii) mean cross-stream geostrophic trans-

port cannot take place, so that eddies are the dominant

driver of tracer transport below the Ekman layer. In

these regions, referred to as the core of the fronts, our

goal is twofold: 1) to quantify the net contribution of the

mesoscale eddy field to cross-frontal tracer transport and

2) to disentangle the respective roles of eddy-advective

and eddy-diffusive components on cross-frontal tracer

transport.

To achieve our goals, we make use of an eddy-rich

ocean–atmosphere climate model coupled to a sim-

plified ocean biogeochemical model [GFDL Climate

Model, version 2.6 (CM2.6)– simplified version of

Biogeochemistry with Light Iron Nutrients and Gas

(miniBLING) model] in order to investigate the role of

resolved mesoscale eddies in transporting tracers across

the core of fronts.We focus on the Polar Front (PF), one

of themain fronts of theACCand the northern boundary

3058 JOURNAL OF PHYS ICAL OCEANOGRAPHY VOLUME 45

of the Antarctic Divergence, which is where most deep

waters upwell. The investigation is carried out in a

preindustrial simulation to avoid the complexity in-

duced by transient forcing, in particular for heat and

carbon. Advection budget terms computed online in the

model allow us to accurately calculate the transport

across the PF core and decompose the transport into

time-mean and eddy components. Details of the model

and methods are provided in section 2. Results are

presented with an emphasis on heat and carbon in sec-

tion 3a. In section 3b, we highlight differences between

tracers arising from the along-isopycnal tracer gradi-

ents. In section 4, we discuss limitations of our ap-

proach. We also compare results for another front, the

Subantarctic Front (SAF), to that of the PF. We close

the paper in section 5 with a summary of the main re-

sults. Finally, we offer two appendices that expand on

the method.

2. Methods

a. Model and simulation

We briefly present here some aspects of the physical

and biogeochemical components of the climate model

used in this study that are of relevance to the cross-

frontal transport of tracers in the Southern Ocean. For

further details, the reader is referred to Delworth et al.

(2012) and Griffies et al. (2015) for a description of the

physical component (CM2.6) and to Galbraith et al.

(2015, manuscript submitted to J. Adv. Model. Earth

Syst.) for a description of the biogeochemical ocean

component (miniBLING).

1) CM2.6–MINIBLING

CM2.6 is a coupled climate model first introduced by

Delworth et al. (2012) and further analyzed by Griffies

et al. (2015). The model uses an atmospheric component

of roughly 50-km horizontal resolution as well as sea ice

and land model components. The oceanic component is

based on the Modular Ocean Model, version 5 (MOM5;

Griffies 2012) run with volume-conserving Boussinesq

kinematics and a z* vertical coordinate. The vertical

resolution is 50 levels with a thickness of 10m at the

surface increasing with depth to 210m. The horizontal

grid spacing is 0.18, corresponding to a grid size of 5.5 kmat 608S. The horizontal resolution is thus fine enough tosimulate a rich mesoscale eddy field in the Southern

Ocean, as shown in Delworth et al. (2012) and Griffies

et al. (2015). However, we note that the mesoscale eddy

spectrum is not fully resolved, in particular near the

coasts and south of 608S (Hallberg 2013). CM2.6 is runwith no lateral tracer diffusion. The submesoscale mixed

layer eddy parameterization of Fox-Kemper et al.

(2011) is applied to account for the restratification ef-

fect of submesoscale eddies in the mixed layer that the

0.18 horizontal grid spacing is not able to resolve.However, no mesoscale eddy transport parameteriza-

tion is used in the tracer equation, so that our study

focuses only on mesoscale processes that are explicitly

resolved in the model.

Because of the computational cost of adding tracers

to a 0.18 coupled climate model, a simplified version ofthe prognostic biogeochemical model Biogeochemistry

with Light IronNutrients andGas (BLING) (Galbraith

et al. 2010), called miniBLING, has been developed.

While the core ecosystem behavior of miniBLING re-

mains identical to BLING, the number of prognostic

tracers has been reduced to three, namely, dissolved

inorganic carbon (DIC), a dissolved inorganic macro-

nutrient (called PO4), and dissolved oxygen (O2). The

macronutrient PO4 is intended to represent the limiting

macronutrient, which is generally NO3 in the real ocean.

Here, it is called PO4 to be clear that it does not include

N2 fixation or denitrification. The reduction of tracers

has been accomplished by eliminating dissolved organic

phosphate via an altered representation of PO4 re-

cycling, with more rapid near-surface recycling of PO4under low PO4 conditions. The BLING prognostic iron

tracer has been replaced with a prescribed monthly iron

climatology computed froma 18 simulation usingBLING.The carbonate equilibria at the ocean’s surface are de-

pendent on prognostic temperature, salinity, and DIC,

with surface alkalinity prescribed at each time step as a

function of model salinity, using a 2D alkalinity–salinity

linear regression based on observed global maps (Garcia

et al. 2010a; Key et al. 2004). MiniBLING uses param-

eter values chosen for BLING based on a 38 globalocean-only simulation, which were not ‘‘tuned’’ for the

0.18 ocean of CM2.6. A detailed description andevaluation of the miniBLING model can be found in

Galbraith et al. (2015, manuscript submitted to J. Adv.

Model. Earth Syst.).

2) PREINDUSTRIAL SIMULATION

A simulation of the CM2.6–miniBLING model is run

with the atmospheric CO2 concentration fixed at

286ppm corresponding to the preindustrial level of the

year 1860. The ocean is started from rest with temper-

ature and salinity fields initialized toWorld Ocean Atlas

2009 (WOA; Garcia et al. 2010a; Locarnini et al. 2010).

PO4 and O2 fields are initialized to WOA (Garcia et al.

2010a,b), and DIC fields are initialized to the Global

Ocean Data Analysis Project (GLODAP) corrected for

preindustrial values (Key et al. 2004). MiniBLING is

included starting at year 48, thus allowing for the


physical circulation to partially adjust. The simulation is

run for 200 yr in total, that is, 152 yr for biogeochemistry.

In this study, the last 20 yr of the simulation (years 181 to

200) are investigated.

3) EVALUATION OF CM2.6–MINIBLING

Here, we briefly compare the simulated physical

transport and tracer distributions with observations.

The simulated transport across Drake Passage stabi-

lizes at around 100 Sverdrups (Sv; 1Sv5 106m3 s21) after;120yr of downward drift (Fig. 1a). This value is lowerthan the observational estimates ranging from 110 to

170Sv (e.g., Whitworth 1983; Whitworth and Peterson

1985; Cunningham et al. 2003; Chidichimo et al. 2014).

The weak ACC transport is most likely related to a lack

of formation and overflow of dense waters formed along

the Antarctic coasts that are not properly represented

in the CM2.6 simulation (see Fig. 1c). A comparison of

meridional sections between the model andWOA (not

shown) reveals that the density structure of the model

collapses at depth south of the ACC due to a lack of

overflow of dense waters formed on the Antarctic

shelves. Inhibited overflows are typical of z-coordinate

models, as noted byWinton et al. (1998) and Legg et al.

(2006). However, within the top 1.5 km of the ACC, the

density structure of the model is similar to the obser-

vations, so that the jet intensity is not affected by the

weak ACC. In addition, the occurrence of twoWeddell

Sea polynya events in the simulation, one starting in

year 127 and the other in year 184 and both lasting

;20 yr, leads to intense deep convection that tempo-rarily boosts the ACC transport by ;10 Sv through an

FIG. 1. (a) Time series of the transport at Drake Passage in the CM2.6–miniBLING simulation. (b) Meridional

overturning circulation in s2 coordinates averaged over the last 20 yr of the CM2.6–miniBLING simulation, with

s2 the potential density referenced at 2000 m. Red cells indicate clockwise flow while blue cells indicate coun-

terclockwise flow with a 2-Sv contour interval. The solid vertical line indicates the mean latitude of the PF with

the dashed lines showing the range of latitudes that the PF occupies. The green line indicates the density of the

zonal maximum of the September mixed layer depth and the gray line indicates the topographic sill depth at the

latitudes of Drake Passage. Note that the mixed layer is very deep south of ;608S due to the occurrence ofa polynya in the Weddell Sea. (c) Transport summed into different water mass classes from (blue) observation-

based estimates, (red) the phase 5 of the CoupledModel Intercomparison Project (CMIP5) multimodel ensemble

mean, and (green) the CM2.6–miniBLING simulation. Transports are estimated in a latitude range of 308 to 408Sin observations and are computed at 308S in models. Error bars show the minimum and maximum of the ob-servation-based datasets (on top of blue bars) and the CMIP5 multimodel standard deviation (on top of red bars)

for each water mass class. The compilation of estimates from observations and the CMIP5 model ensemble, and

themethod used to findwater mass boundaries, are described in Sallée et al. (2013). A similar methodwas appliedto the last 20 yr of CM2.6–miniBLING output.


increase in the meridional pressure gradient, as re-

ported in previous modeling studies (Hirabara et al.

2012; Shakespeare and Hogg 2012; Cheon et al. 2014;

Spence et al. 2014).

The meridional overturning circulation (MOC) av-

eraged over the last 20 yr of the simulation shows a

maximumof;20 Sv in the subtropical cell,;20 Sv in thesubpolar cell, and ;10 Sv in the bottom cell (Fig. 1b).These cells correspond respectively to light subtropical

waters flowing to the south and being transformed into

SAMW as they cool (subtropical cell); upper circum-

polar deep waters (UCDW) flowing southward and

upward and being transformed into AAIW and SAMW

by surface fluxes (subpolar cell); and lower circumpolar

deep waters (LCDW) flowing farther south, trans-

forming into dense waters through heat loss and brine

rejection near the Antarctic coasts, and then sinking

before becoming Antarctic Bottom Waters (AABW)

(bottom cell). These transports lie well within the broad

range of model estimates (subtropical cell:211 to 30 Sv;subpolar cell: 8 to 18Sv; bottom cell:23 to220 Sv; e.g.,Hallberg and Gnanadesikan 2006; Ballarotta et al. 2013;

Dufour et al. 2012). However, there is less agreement

with observation-based estimates, as the main return

path for circumpolar deep waters in the model is

through the formation of AAIW, whereas observational

estimates suggest more transforms into AABW

(Fig. 1c). This is a feature shared by many models, as

highlighted in previous studies (Downes et al. 2011;

Sallée et al. 2013).The simulation is initialized with observational cli-

matologies [see section 2a(2)] that provide a reference

to evaluate how the model drifts from its initial state.

Figure 2 shows a comparison between these observa-

tional climatologies and the last 20 yr of the simulation

for surface temperature, salinity, DIC, PO4, and O2.

While the large-scale patterns and values of the simu-

lated variables are overall in good agreement with ob-

servations, some discrepancies exist. The simulation is

generally cooler than observations at the surface, an

expected difference as the simulation does not experi-

ence the climate warming of the industrial era. The

simulation is also generally fresher than observations at

the surface. A strong warm and saline anomaly with

respect to observations shows up in the Weddell Gyre

and eastward up to 1508E because of relatively warmand saline deep waters reaching the surface during the

Weddell Sea polynya that occurs in the last 20 yr of the

simulation. Anomalies associated with the occurrence of

the Weddell Sea polynya are also noticeable in the

biogeochemical tracer fields.

Except along Antarctic coasts, DIC and PO4 concen-

trations south of 408S are higher in the simulation, while

O2 shows the opposite bias. The major reason for those

biases seems to be an overexpression of the iron limita-

tion in the modeled Southern Ocean (Galbraith et al.

2015, manuscript submitted to J. Adv. Model. Earth

Syst.). The departure from observations may also be at-

tributed to the (i) location of the wind-driven upwelling

bringing tracers to the surface more equatorward in the

simulation and (ii) observations being scarce and biased

toward summer (that is low forDIC and PO4 and high for

O2), in particular south of 608S.The ocean component of CM2.6 provides finescale

circulation features such as boundary currents, inter-

actions between jets and topography, and mesoscale

eddy fields. However, because of time and computa-

tional constraints, the experimental design suffers from

two main drawbacks: (i) the model is still drifting due to

the relatively short length of the simulation and

(ii) there was a lack of extensive evaluation and tuning of

miniBLING during the development stage of the model.

Running CM2.6 under a 1990 constant radiative forcing,

Griffies et al. (2015) showed that the temperature drift

was significantly reduced compared to previous coarser-

resolution versions of the model, with drift reduction

arising from the rich mesoscale eddy field in CM2.6.

Moreover, one advantage of this brief simulation length

is to prevent the physical and biogeochemical fields from

drifting far away from the initial conditions. Finally, the

fully prognostic implementation provides internally

consistent physical–biogeochemical coupling. Hence,

CM2.6–miniBLINGprovides an adequate framework in

which to investigate the effect of finescale resolved

processes, including mesoscale eddies, on physical and

biogeochemical tracer transport.

b. Definition of ACC front paths

Fronts are boundaries separating regions of differing

watermass characteristics.When these fronts have strong

density gradients, they coincide with intense geostrophic

currents, called jets, that tend to act as barriers to mixing.

Traditionally, fronts have been identified using interior

hydrographic properties (Orsi et al. 1995), but the advent

of high-resolution satellite data has promoted the use of

criteria based on sea surface temperature (SST) or sea

surface height (SSH) to detect the associated jets (Gille

1994; Sokolov and Rintoul 2007; Sallée et al. 2008a).While defining fronts from hydrographic properties em-

phasizes their persistent nature as barriers between re-

gions of different biophysical properties, defining them

from dynamical properties highlights their variable na-

ture as intense jetlike features steered by topographic

obstacles. Among the various methods of front detection

that have been developed over the last decades, we

chose a ‘‘contour’’ method based on a hybrid fitting


FIG. 2. Surface fields for (left) observations, (center) the average over the last 20 yr of the CM2.6–miniBLING simulation, and (right)

the difference between the CM2.6–miniBLING simulation and observations. (top to bottom) Temperature (8C), salinity, and DIC, PO4,and O2 (all mmol kg

21). Observation fields of temperature, salinity, PO4, and O2 are from the World Ocean Atlas 2009 (Locarnini et al.

2010; Garcia et al. 2010a,b) and DIC is from GLODAP corrected to preindustrial values (Key et al. 2004). These observational fields are

the ones used to initialize the CM2.6–miniBLING preindustrial simulation and are thus interpolated onto the CM2.6 grid.


procedure (e.g., Sallée et al. 2008a; Dufour et al. 2011;Langlais et al. 2011;Dufour et al. 2013) that reconciles the

hydrographic and dynamical views of the fronts (Langlais

et al. 2011; Chapman 2014).More precisely, for each front

the method identifies a single SSH contour based on hy-

drographic criteria (e.g., temperature and salinity) and

dynamic criteria (e.g., transport and SSH gradients).

For a review and comparison of the strength and weak-

nesses of the various jet detection methods, the reader is

referred to Chapman (2014).

Our study will focus on one of the main fronts of the

ACC, the PF, which shows strong horizontal property

gradients and carries a significant part of the ACC

transport. The transport of tracers across the SAF was

also investigated in this study, leading generally to

similar conclusions. Major differences between the two

fronts will be briefly discussed in section 4.

The PF is usually defined as the location of the north-

ernmost extent of Antarctic Winter Water (AAWW),

identified by the 28C isotherm at around 200-m depth(Belkin and Gordon 1996). We investigated 10 meridio-

nal sections (08E, 308E, 708E, 1158E, 1408E, 1708E,1708W, 908W, 658W, and 428W) of the 20-yr averagemodel fields, where these sections were taken at the po-

sition of several World Ocean Circulation Experiment

(WOCE) hydrographic lines (Orsi and Whitworth 2005).

For each section, we identified a SSH value corre-

sponding to the location of the PF from hydrography

(temperature) and the most intense local meridional

gradients of SSH (Fig. 3). This procedure provided

10 SSH values that were averaged to give the contour

SSH(PF) 5 20.95m.Though specific to our simulation, the SSH contour

value found is consistent with previous modeling studies

(e.g., Langlais et al. 2011). The front detection method

was only applied to 10 meridional sections whose SSH

contour values were then generalized to the circumpolar

ocean by way of averaging. To check the generalization,

we plotted the monthly climatology of the PF positions

represented by the 20.95-m SSH contour on top of thelateral mean SSH gradients (Fig. 4). The seasonal posi-

tions of the PF show good agreement with intense local

SSH gradients in most regions of the Southern Ocean.

Mismatches are generally related to the SSH contour

only following one of the several branches that form the

PF as well as its inability to follow the splitting of the

fronts that generally occurs downstream of topographic

obstacles (e.g., Campbell Plateau). We note that the

strong SSH gradients located north of the PF (e.g., at

Campbell Plateau) correspond to the position of the

FIG. 3. Example of the front detection procedure for a meridional section at 1158E (corresponding to the I9WOCE section). The 20-yr-averaged (a) temperature, (b) meridional SSH gradient, and (c) SSH. (a) The black

solid contour corresponds to the 28C isotherm. The black dashed line indicates the latitude matching the north-ernmost extent of AAWW and a local maximum of SSH meridional gradient. The red dashed line in (c) shows the

SSH value (20.92 m) corresponding to the latitude selected from (a) and (b). Note that this SSH value is specific tothe meridional section at 1158E.


SAF that carries most of the ACC transport in those re-

gions (e.g., Sokolov and Rintoul 2007). Mismatches rep-

resent an inherent limitation of the contourmethod, which

assumes that fronts are single well-defined circumpolar

jets. Nonetheless, we need a circumpolar definition of

fronts that represents their climatological position to cal-

culate cross-frontal transport of tracers in the model.

Moreover, this method allows us to link jets (which can

suppress mixing) with fronts (which separate water

masses), so that implications for heat, carbon, oxygen, and

nutrients reservoirs can be more easily determined. SSH

contours have also been shown to adequately represent

both the mean path and mesoscale activity (meanders and

eddies) of fronts, in particular the meridional deflection

that fronts undergo when encountering a topographic

obstacle (Langlais et al. 2011), and to be more suitable

than other methods for high-resolution studies (Chapman

2014). Finally, we note that while the features of the cross-

frontal tracer transport are independent of the choice of

the variable (e.g., SSH, dynamic height anomaly) used to

define the front position, the alongfront and depth-

integrated cross-frontal tracer transport is sensitive to the

exact path of the contour, as highlighted by Peña Molinoet al. (2014).

c. Computation of cross-frontal transportcomponents

1) METHOD

To compute mass (tracer) transport F across a sec-tion of a given front, meridional and zonal advective

fluxes of mass (tracer) are integrated along the front

(see appendix A for more details). The calculation is

performed at every vertical level and bin of longitude in

the model (i.e., at every 0.18, which is the horizontalgrid resolution).

Although the ACC fronts are known to be tightly

steered by topography, their positions can vary in time,

in particular in flat-bottomed areas or near topographic

obstacles due to mesoscale activities or atmospheric

forcing (Sallée et al. 2008a; Graham et al. 2012). Fol-lowing Kwon et al. (2013), who reported the importance

of accounting for the seasonal migration of density

outcrops when computing subduction rates, the seasonal

migration of fronts is accounted for in our calculation of

the cross-frontal transport. To do so, a 20-yr monthly

climatology of the PF position is created based on the

20-yr monthly climatology of the modeled SSH, using

FIG. 4. Central panel shows the lateral gradients of 20-yr-averaged SSH (j=SSHj, colors, dimensionless), with red corresponding tointense j=SSHj, and 20-yr monthly climatology of the PF positions from the CM2.6–miniBLING simulation, with each black contourcorresponding to amonth. The PF position corresponds to SSH520.95m. The exterior panels show close-up views of the central panel atvarious regions along the front.


the contour defined in section 2b [SSH(PF)520.95 m].If we take January for example, this means that all the

January transports are computed across the 20-yr Jan-

uary climatology of the front position, hence ensuring

that the transport is not influenced by the climatological

seasonal migration of the front. Figure 4 shows the

monthly climatology of the PF position. While front

paths are almost time invariant where fronts meet major

topographic obstacles [e.g., Drake Passage (708W) andCampbell Plateau (2008W)], they show more spatialvariability upstream and downstream of these obstacles

[e.g., downstream of Campbell Plateau or Kerguelen

Plateau (708E)] or where the bottom topography is flat[e.g., eastern Pacific abyssal plains (1708W) and Zapiolabasin (408W)], with a seasonal amplitude reaching ;58of latitude in some places.

2) TRANSPORT COMPONENTS

Following Ballarotta et al. (2013), Bryan et al. (2013),

and Griffies et al. (2015), we compute the mesoscale

eddy component of the transport across a given front

Feddy for every month from

Feddy

5Ftotal

2Fmean

, (1)

where Ftotal is the total1 component of the cross-frontal

transport, andFmean is its time-mean component. Let ustake January once more as an example. To getFtotal, weuse the meridional and zonal advective fluxes of the

tracers calculated online at every time step of the model

and output at monthly period (see appendix A). Cal-

culation of the transport from these online terms is done

every January over the last 20 yr of the simulation. To

getFmean, we use advective terms computed offline fromthe 20-yr-averaged January output of tracer and velocity

fields. Hence, Ftotal includes all the temporal correla-tions between tracer and velocity fields, while Fmeanincludes the temporal correlations between the 20-yr

monthly climatologies of these fields. As a result, Feddyincludes all the temporal fluctuations departing from the

20-yr monthly mean climatology of cross-frontal trans-

port. More details on this decomposition can be found in

appendix B of Griffies et al. (2015).

Using this method, we are thus able to capture the

variety of processes resolved in the model that contrib-

ute to the tracer transport across the climatological po-

sition of the fronts. Some of those processes can be

observed on the daily snapshot of surface DIC south of

Africa shown in Fig. 5, along with the mean position of

the PF. Tracer and velocity anomalies at the climato-

logical front position that result from instantaneous

fluctuations of the front, rings detaching from the front

edges, or waves propagating across the fronts are all

accounted for in the cross-frontal transport calculation

and fall into the mesoscale eddy component Feddy.Hence, mesoscale eddies should be understood here in

the broad sense of transient mesoscale activity (mean-

ders, rings, waves, etc.). More details on the kinematic

interpretation of transport across a climatological front

position can be found in appendix A.

d. Representation of fronts in the vertical

In the following, we use potential density referenced to

2000m (s2) to bin tracers and transports (see appendixB)

and to define the vertical extension of the jets as well as

the Ekman layer. The quantity s2 is preferred over depth

as it is more consistent with water mass properties and

over s1, as we generally display results for the whole

water column. This choice also has the advantage of

comparability with the many other modeling studies that

use s2 when investigating transport binned into density

layers (e.g., Lee et al. 2007; Ballarotta et al. 2013).

Though jets are deep reaching in the Southern Ocean,

sometimes extending down to the ocean floor (e.g.,

Graham et al. 2012), intense jets aremostly confined to the

upper 1–1.5km (Smith and Marshall 2009; Abernathey

et al. 2010), and thus generally lie above the sill of major

topographic obstacles (;2km; see Fig. 6). At these depthsand where the jet is unbounded, Ekman transport and

FIG. 5. The 20-yr-averaged position of the PF (black solid

line) over a daily snapshot of surface DIC concentrations south

of Africa. Note the variety of mesoscale features in the DIC

field, including rings detaching from the front edge and finescale

meandering of the DIC field around the climatological front

position.

1 In the following, total is used for the sum of the time-mean and

eddy components, while net is used for the sum of northward and

southward transports.


mesoscale eddies are the main conveyers of tracer trans-

port across the front. The lower boundary of the front core

is thus defined here as the depth that lies just above the

deep southward geostrophic transport, which is restricted

to below the sill of major topographic obstacles. Based on

the time-mean component of themass transport across the

PF binned into s2 coordinates (Fig. 7c1, blue line), s2 536.9kgm23 is chosen as the deepest extension of the PF

core (Figs. 6 and 7c1, solid lines). Though the ocean is

weakly stratified in this density range,meaning that a small

change in s2 corresponds to a large change in depth, we

note that our conclusions are not very sensitive to the s2value chosen (e.g., s2 5 37.0kgm

23 would give very

similar results). Figure 6 shows that s2 5 36.9kgm23 de-

limits the vertical extension of the intense jets that form the

model PF and that lie above the sill of major topographic

obstacles at a depth of around 1.5km, in agreement with

observations (e.g., Smith and Marshall 2009). We note

however that the model PF intersects topography above

36.9kgm23 at the Kerguelen Plateau (;708E), inducing aweak geostrophic transport within the PF core as we will

see in section 3.

Previous studies have reported that while transport is

inhibited across the core of the jet, the Ekman layer

remains a region of vigorous cross-frontal transport

(e.g., Palter et al. 2013). To investigate the role of vari-

ous transport components in the cross-frontal transport

of tracers, we divided the frontal core region into two

layers, corresponding to the Ekman layer and below the

Ekman layer, that is, from the base of the Ekman layer

down to the lower boundary of the front core. Based on

the total component of the mass transport across the PF

binned into s2 coordinates (Fig. 7c1, black line),

s2 5 36.4 kgm23 is chosen as the deepest extension of

the Ekman layer (Figs. 6a and 7c1, dashed lines). The

s2 5 36.4 kgm23 delimits the near-surface layer where

the total transport is primarily driven by the time-mean

transport (Fig. 7c1, blue line), that is, mostly by the

Ekman transport. In the model, the alongfront aver-

age depth of s25 36.4 kgm23 ranges from around 140-

to 200-m depth over the seasons. As our cross-frontal

transport calculation captures the seasonal cycle

(section 2c), the transport we compute is expected to be

carriedwithin different density ranges in different seasons.

The s2 5 36.4kgm23 thus corresponds to the densest

waters lying within the winter Ekman layer. Finally, we

note that the s2 chosen to define the lower boundaries of

the Ekman layer and the jet core are specific to the PF.

3. Results

a. Eddy contribution to cross-frontal tracer transport

We start our analysis by investigating the net (i.e., sum

of northward and southward transports) effect of eddies

on the total (i.e., sum of the time-mean and eddy com-

ponents) transport of tracers across the PF core. We

then explore the regions where the cross-frontal trans-

port is favored and investigate the importance of these

regions for the net transfer of tracers across the PF. In

the following, results are presented in the three layers

defined in section 2d, that is, (i) the entire core of the PF,

subdivided into (ii) the Ekman layer, and (iii) below the

Ekman layer.

FIG. 6. The 20-yr-averaged current speed (m s21) from the CM2.6–miniBLING simulation (a) along the path of the

PF and (b) across Drake Passage at 608W. The solid white line shows s2 5 36.9 kgm23, the isopycnal chosen as the

lower boundary of the PF core, with s2 the potential density referenced at 2000m. (a) The white dashed line shows

s25 36.4 kgm23, the isopycnal chosen as the lower boundary of the Ekman layer (see section 2d for further details).

The vertical white dotted lines correspond to the location of (a) Drake Passage (608W) and (b) the PF. Note that thejets are only intense in some locations, as also visible in Fig. 4.


1) THE BALANCE OF TRANSPORT COMPONENTSACROSS THE PF

Figure 7 shows the 20-yr average of temperature

and DIC fields along the PF (Fig. 7a) and the mass,

temperature, and DIC transports across the PF as a

cumulative sum (Fig. 7b) or sum (Fig. 7c) along the

front. Each transport is binned into s2 layers along

the path of the PF. By definition (section 2d), the

total cross-frontal transport is mainly northward in

the Ekman layer and southward below. Below the PF

core (s2$ 36.9 kgm23, horizontal black line in Fig. 7), a

geostrophic current transports deep waters southward,

providing a net flux of heat, carbon, oxygen, and nutri-

ents to high latitudes. A weak geostrophic current

transports AABW northward in the deepest s2 layers

(Figs. 7b,c), allowing for a northward flux of tracers in

the abyss.

FIG. 7. The 20-yr-averaged tracer distributions and transports across the PF against s2. (a) Temperature andDIC along the PF binned

into s2 layers. (b) Mass, temperature, and DIC transports across the PF cumulatively summed along the front for every s2 layer.

(c) Mass, temperature, and DIC transports across the PF summed along s2 layers with the total transport (black) deconvolved into its

time-mean component (blue) and transient eddy component (red). Transport scales are dependent on the size of s2 bins. The reader is

thus referred to Fig. 8 to get a sense of how large the transports are. Positive transports are northward. Temperature transport (Sv 8C) isexpressed as heat transport equivalent in TW. Vertical profiles have been smoothed with a low-pass filter. This results in different

minima andmaxima in the transports of (b) and (c). The black dashed linemarks the base of the Ekman layer (s25 36.4 kgm23) and the

black solid line the lower extension of the PF core (s2 5 36.9 kg m23). Details of how the limits of the PF core and the Ekman layer are

chosen are provided in section 2d.


We now return to the PF core (s2 # 36.9 kgm23), the

region of our focus. Within the Ekman layer, the cross-

frontal transport of mass is northward and is driven by

the time-mean component, that is, mainly the Ekman

transport, with some compensation from eddies

(Fig. 7c1). Below the Ekman layer and down to the

bottom of the PF core, the cross-frontal transport is

mainly southward and weaker than in the Ekman layer.

Here, the eddy component is the main driver of the total

cross-frontal transport, with little contribution from the

time-mean component. This eddy-driven regime that

lies between the Ekman-driven and geostrophy-driven

regimes is consistent with the traditional zonally aver-

aged picture of momentum balance at the latitudes of

Drake Passage (e.g., Olbers et al. 2004; Marshall and

Speer 2012). Departure from this balance mainly in-

volves the incursion of geostrophic transports into the

eddy-driven regime. We identify two main sources of

geostrophic transports within the PF core: the in-

tersection of the PF core with the Kerguelen Plateau

(Fig. 6a) and the deviation of the mean flow from the

surface flow with depth (see next section). Another

source of geostrophic transports might arise from the

intersection of some PF core isopycnals with the ocean

surface as discussed in Mazloff et al. (2013). Transports

look quite different when averaged along latitude circles

instead of along the front (see Fig. 1b). As Treguier et al.

(2007) showed, calculating the transport across mean

streamlines rather than latitude circles more effectively

reveals the physical nature of the meridional over-

turning in the upper ocean. In particular, averaging

along streamlines removes the effect of stationary me-

anders that show a large contribution to the transport

averaged along latitude circles (e.g., Treguier et al. 2007;

Dufour et al. 2012). Though our frontwise SSH co-

ordinate does not correspond to streamlines, it

provides a proxy for the flow path with the best agree-

ment being at the surface (i.e., the SSH contour follows

the surface geostrophic flow).

Similarities in Fig. 7b show that temperature and DIC

cross-frontal transports are closely following mass trans-

port (see also Fig. 9). As temperature and DIC advective

transports have the same sign as mass transport, those

similarities suggest that eddy-diffusive transport either

reinforces the advective transport or is small enough so

that it does not change the sign of the transport. This

point will be further discussed in section 3b. However,

Figs. 7c1–c2 reveals that the alongfront sum of cross-

frontal temperature transport differs significantly from

that of mass. The key difference is that temperature

transport is enhanced in the upper layers. In contrast, the

alongfront sum of cross-frontal DIC transport is very

similar to that of mass (Figs. 7c1,c3), as are the alongfront

sum of cross-frontal PO4 and O2 transports (not shown).

Differences between cross-frontal transport of tempera-

ture and biogeochemical tracers arise from the vertical

gradient of temperature [(›Q/›s2)/Qmin; Fig. 7a2) beingaround 10 times greater than that of biogeochemical

tracers [e.g., (›DIC/›s2)/DICmin; Fig. 7a3] because of the

temperature transport being expressed in degrees Celsius

(see appendix A).

Figure 8 presents an integrated view of the cross-

frontal transports of Fig. 7c formass and the four tracers,

here partitioned into the three layers defined in section

2d. Within the PF core, the sum of the total cross-frontal

transport is northward for all tracers. This transport is a

result of (i) strong northward transport in the Ekman

layer, dominated by Ekman transport with partial com-

pensation from the eddy component, and (ii) a more

modest (;4 times smaller) southward transport belowthe Ekman layer, dominated by eddy transport with very

little contribution from the time-mean geostrophic

transport as noted in Fig. 7c. Thus, transport across the

PF core is dominated by the northward Ekman flow,

with eddies providing a significant southward transport

that drives the total transport below the Ekman layer.

The imbalance between the northward time-mean trans-

port and the southward eddy transport in Fig. 8 indicates

that the upper cell of the MOC is mostly closed below the

PF core. Eddy transports are found to provide around 40%

of the southward flow that closes the upper cell and to be

located primarily above the sill depth ofmajor topographic

ridges. The remaining (;60%) is provided by geostrophictransports. This result contrasts with the more traditional

picture of an upper cell mostly closed by eddy transports

above topographic ridges, as conveyed in particular by

idealized studies or tracer inversion [e.g., Lumpkin and

Speer (2007); see also the review of Marshall and Speer

(2012)]. However, we note that our result is consistent with

Mazloff et al. (2013).

Over the entire depth of the PF, we estimate that

eddies support around one-third of the southward mass

transport with the remaining two-thirds being supported

by geostrophic currents. Eddies are also found to sup-

port more than two-thirds of the southward temperature

transport, with more than 80% achieved within the PF

core. This predominance of eddies in transporting tem-

perature southward with weak but significant contribu-

tion from geostrophic currents is in agreement with

previous observational and modeling studies (e.g., de

Szoeke and Levine 1981; Peña Molino et al. 2014).

2) HOTSPOTS OF TRACER TRANSPORT

The alongfront spatial variability in the cross-frontal

transport is shown in Fig. 9. Here, we show the topog-

raphy in the model (Fig. 9a) and the 20-yr-averaged


components of the transport across the core of the PF

(s2# 36.9 kgm23) at every 0.18 of longitude (Fig. 9b) for

mass, temperature, andDIC. Both time-mean and eddy

components are enhanced where the front encounters

major topographic obstacles, namely, at the Southeast

Indian Ridge, Campbell Plateau, Macquarie Ridge,

East Pacific Rise, Drake Passage, Mid-Atlantic Ridge,

Southwest Indian Ridge, and Kerguelen Plateau

(Fig. 9b). The PO4 and O2 transports exhibit very similar

features (not shown) to that of mass and DIC transports

in these hotspots. At every 0.18 of longitude, the time-mean component drives a large part of the total transport

across the PF, with the eddy component being less than

20% of the time-mean component (Fig. 9b). This feature

holds for mass and biogeochemical tracers but not for

temperature, whose eddy component shows amplitudes

twice as large as those for mass and DIC. Despite the

minor local contributions of the eddy component, when

transport is summed along the PF, the eddy contribution

to the total cross-frontal transport is of the same magni-

tude as its time-mean counterpart, as noted in Fig. 8.

Any advective flux contains rotational and divergent

components (e.g., Marshall and Shutts 1981; Roberts

and Marshall 2000; Fox-Kemper et al. 2003; Bishop

2013). However, there is no unique decomposition of

such a flux into rotational and divergent components

(Fox-Kemper et al. 2003). Although we do not attempt

to perform such a decomposition here, we infer a non-

trivial rotational component in regions of active eddies,

such as near topography. In Fig. 9b, the cross-frontal

FIG. 8. The 20-yr averages of the transport of mass, temperature, DIC, PO4, and O2 across the PF, horizontally integrated along the PF

and vertically integrated within (a) the PF core (s2 # 36.9 kgm23), then separated into the (b) Ekman layer (s2 # 36.4 kgm

23), and

(c) below the Ekman layer (36.4 kgm23, s2# 36.9 kgm23). Note the difference in scales between (c) and (a) and (b). Details of how the

limits of the PF core and the Ekman layer are chosen are provided in section 2d. The total transport (black) is deconvolved into its time-

mean component (blue) and its transient eddy component (red). Positive transports are northward. Temperature transport (Sv 8C) isexpressed as heat transport equivalent in PW.


transport indeed exhibits rather large fluctuations at

hotspots. Integrating over a portion of the front allows

some cancellation of the rotational component, though

the rotational component cannot be perfectly removed

by way of averaging (Griesel et al. 2009). Here, we

investigate the divergent component of the cross-frontal

transport by computing the alongfront cumulative sum of

the cross-frontal transport in the three layers (Figs. 9c–e).

Note that when integrating around Antarctica, the rota-

tional component of the flux vanishes (integral along a

FIG. 9. Geographic distribution of cross-frontal transport of mass, temperature, andDIC. (a)Model topography (background black and

white) and (a2),(a3) 20-yr-averaged tracer at the PF (colored contours). Tracers in (a2)–(a3) are averaged vertically between the surface

ocean and the lower extension of the PF core (s2# 36.9 kgm23). (b) The 20-yr-averaged transport across the PF at every 0.18 of longitude.

The 20-yr-averaged transport across the PF cumulatively summed along the front. The total transport (black) is deconvolved into its time-

mean component (blue) and its transient eddy component (red). Transports are integrated vertically between (c) the surface ocean and the

lower extension of the PF core (s2 # 36.9 kgm23) and then separated into (d) the Ekman layer (s2 # 36.4 kgm

23) and (e) below the

Ekman layer (36.4 kgm23 , s2 # 36.9 kgm23). Note the difference in scales between (c),(d) and (e). Details of how the limits of the PF

core and the Ekman layer are chosen are provided in section 2d. Positive transports are northward. Temperature transport (Sv 8C) isexpressed as heat transport equivalent in PW.


closed contour) so that the sums presented in Figs. 8 and 9

correspond to the divergent part of the flux only.

In the Ekman layer (Fig. 9d), the time-mean compo-

nent displays a smooth positive slope, reflecting the

Ekman flow that drives northward cross-frontal trans-

port all along the PF, consistently exporting waters and

their tracer content northward. Below the Ekman layer

(Fig. 9e), the time-mean component shows large fluc-

tuations that intensify where the PF flows around major

topographic obstacles (e.g., Campbell Plateau and

Drake Passage). Large fluctuations in the time-mean

component of the cross-frontal transport mainly result

from a lack of alignment between the mean flow and the

SSH contour used to define the front. Deviations of the

mean flow from the surface flow have been shown to

increase with depth and to be enhanced where the front

develops large meanders due to interaction with to-

pography (Peña Molino et al. 2014; Phillips and Bindoff2014). This deviation is a result of the ACC being non-

equivalent barotropic (i.e., deep flow not parallel and

not proportional to the surface flow). Deviations of the

mean flow are known to support a significant transport

across the front (Peña Molino et al. 2014). For instance,in the Ekman layer, the time-mean mass transport

across the PF (27.7 Sv; Fig. 8b1) results from a north-

ward transport of 32.1 Sv by the Ekman flow and a

poleward transport of 4.4 Sv by deviations of the mean

geostrophic flow from the surface flow. This mean geo-

strophic cross-frontal transport results from the near

cancellation between large zonal and meridional com-

ponents [O(50) Sv].

We now examine the divergent component of the

cross-frontal transport for the eddy component. The

eddy component shows a marked steplike behavior in

each layer (Figs. 9c–e), indicating that the eddy

transport is strongly enhanced at and near major to-

pographic obstacles (i.e., at hotspots of tracer trans-

port) and very small elsewhere. This behavior of the

eddies contrasts to the time-mean component, which

contributes to the total cross-frontal transport all

along the PF. Intensification of the eddy component

thus occurs in the vicinity of major topographic ob-

stacles where the mean flow is strong and meandering,

as shown by both the intense mean current speed

(Fig. 6) and sharp lateral gradients of SSH (Fig. 4).

Naveira Garabato et al. (2011) hypothesized the link

between regions of large mean flow strain and hot-

spots of transport or leaky jet segments in the ACC. In

such regions where large-scale standing meanders

develop, baroclinicity of the mean flow is increased

through topographic steering, leading to enhanced

baroclinic instability that intensifies eddy-advective

activity (Thompson and Sallée 2012). Topographic

steering of the mean flow also sharpens the cross-

frontal tracer gradient as the jet narrows, potentially

increasing the eddy-diffusive activity. Finally, stand-

ing meanders distort the front meridionally, in-

creasing the surface of exchange at the front. These

ideas have been hypothesized or discussed in several

recent studies, which all tend to show that eddy ac-

tivity is augmented in the presence of standing me-

anders (Naveira Garabato et al. 2011; Thompson and

Sallée 2012; Zika et al. 2013; Abernathey and Cessi2014). In particular, using numerical simulations with

and without topography, Abernathey and Cessi (2014)

showed that cross-frontal eddy heat flux was stronger

in the experiment with topography due to the pres-

ence of standing meanders.

3) EFFECT OF HOTSPOTS ON THE TOTALTRANSPORT

In between topographic obstacles, the time-mean

component dominates the total transport driving a

northward transport, as indicated by the smooth pos-

itive slope in Fig. 9c. At major topographic features,

the southward eddy transport intensely opposes the

Ekman transport, thus reducing the net northward

cross-frontal transport or driving a net southward

transport, as highlighted by the steplike features in

Fig. 9c. In particular, the total transport displays

strong southward deflections downstream of Drake

Passage, Kerguelen Plateau, and the Southwest Indian

Ridge. In these regions where the PF encounters large

topographic obstacles, intense eddy activity has been

reported (e.g., Meredith and Hogg 2006; Morrow et al.

2010). Drake Passage is where the PF develops its

largest meridional excursion, leading to increased

baroclinic instability and a large surface of exchange

across the front, two conditions that favor increased

eddy contribution. At the Southwest Indian Ridge,

observational studies have reported the presence of a

warm eddy corridor that allows some eddies to cross

the PF and transport heat to the Antarctic zone (e.g.,

Gouretski and Danilov 1994; Ansorge et al. 2014).

Hence, our diagnostics show that eddies induce a

southward cross-frontal transport of tracers all along the

PF, partially compensating the northward Ekman trans-

port in the Ekman layer and dominating the total trans-

port in the PF core below the Ekman layer. At major

topographic obstacles, however, the enhanced eddy ac-

tivity drives a southward total cross-frontal transport

throughout the PF core. Hence, we conclude that it is in

the regions between topographic obstacles that upwelled

water or tracers are returned to the north. In contrast,

hotspots are privileged pathways for the transport of

water and tracers to the south.


b. Advective versus diffusive role of eddies

Eddies act to move tracers along isopycnals via two

mechanisms: eddy-advective transport [also called the

Gent and McWilliams (1990) effect], resulting from

extraction of available potential energy from the un-

stable mean flow, and eddy-diffusive transport (also

called isopycnal or neutral diffusion), resulting from

eddies stirring tracers along isopycnals to be eventually

mixed by small-scale processes. While the eddy tracer

diffusive transport is downgradient in steady state, the

eddy tracer advective component can be either upgra-

dient or downgradient, depending on the large-scale

tracer distribution with respect to dynamical circula-

tion. Hence, eddy-advective and eddy-diffusive trans-

ports can either reinforce or oppose each other. Here,

we compare eddy cross-frontal transport for mass,

temperature, DIC, PO4, and O2 and provide a scaling

of the eddy-diffusive transport for each tracer to infer

the relative importance of eddy-advective and eddy-

diffusive transports.

1) COMPARISON OF EDDY CROSS-FRONTALTRANSPORTS BETWEEN TRACERS

As seen in Fig. 8, all tracers present the same general

picture as mass. That is, for each layer, the balance be-

tween transport components is similar in terms of sign

and relative magnitude. The eddy components of the

cross-frontal transport of mass and tracers also present

very similar features, both regarding spatial patterns

(i.e., transports increase/decrease at the same locations)

and sign (i.e., transports oppose/reinforce the time-

mean component; see Figs. 7 and 9). Considering that

mass is only advected (no diffusion), these similarities

suggest that eddy-diffusive transport is negligible or al-

ternatively that eddy-diffusive and eddy-advective

transports reinforce each other. In the following, we

explore these two scenarios.

Despite similarities in the eddy components of mass

and tracer transports, Fig. 8 shows that the degree to

which eddies oppose the time-mean transport varies

significantly between mass and tracers as well as among

tracers (see also Figs. 7 and 9). There are two ways for

the ratio of the eddy to the time-mean transport of

tracers to differ from that of mass. First, the spatial

distribution of the tracers may increase the contribution

from one transport component over the other. If tracers

were uniformly distributed in the ocean, the ratio would

be the same for mass and the tracers. However, tracers

have nonuniform alongfront and vertical distributions

(Figs. 7a, 9a), and time-mean and eddy components are

predominant at different locations and depths, so that

the ratio is likely to be different between mass and

tracers as well as between tracers. For instance, tracers

whose concentration decreases with depth, like tem-

perature and O2, are likely to have a lower ratio than

tracers whose concentration increases with depth, like

DICandPO4, because time-mean transport across the PF

core is only large in the Ekman layer. Second, the ratio

can vary between mass and tracers because the cross-

frontal isopycnal tracer gradient may support an eddy-

diffusive transport that either opposes or reinforces the

eddy-advective transport. If the tracers were uniformly

distributed on the isopycnals, eddy-diffusive transport

would be zero so that the eddy-advective component

would be the only contributor to eddy transport, as is the

case for mass.

2) ALONG-ISOPYCNAL TRACER GRADIENTS

Several studies have proposed a simple rule to de-

termine the direction of eddy-diffusive transport by ex-

amining the relative slopes of tracers and isopycnals

(e.g., Gregory 2000; Lee et al. 2007). Figures 10a1–d1

shows temperature, DIC, PO4, and O2 binned in (SSH;

s2) space in the region of the PF. At the PF, temperature

is generally warmer in the light layers and cooler in the

deep layers but shows an inversion between 36.2 and

36.6 kgm23, which is the signature of cold and fresh

AAWW extending from the south to the PF (Fig. 10a1).

DIC concentrations increase with depth (Fig. 10b1), as

do PO4 concentrations except between 36.5 and

36.7 kgm23, where a local maximum of PO4 lies just

above a local minimum (Fig. 10c1). Finally, O2 concen-

trations decrease with depth except in the density range

of the PO4 maximum where O2 shows a local minimum

(Fig. 10d1). These local extrema correspond to the

nutrient-rich and oxygen-poor UCDW and the nutrient-

poorer LCDW, respectively, in agreement with obser-

vations (e.g., Orsi and Whitworth 2005).

Comparing the relative slopes of tracer isosurfaces

and isopycnals, we note that the isotherms are gener-

ally steeper than isopycnals, in particular between

around 36.2 and 36.7 kgm23, indicating that the cross-

frontal isopycnal temperature gradient is intense in

these layers (Fig. 10a1). In contrast, biogeochemical

tracer isosurfaces are closely aligned with isopycnals

below 36.2kgm23, indicating weak cross-frontal iso-

pycnal gradients (Figs. 10b1–d1). This close alignment

holds in particular for DIC and PO4, while O2 isosurfaces

show significant slopes between 36.0 and 36.5kgm23. The

steepness of isotherms relative to isopycnals is typical of

the SouthernOcean, where density is partly controlled by

salinity and the vertical gradient of temperature is rela-

tively weak, leading to a northward along-isopycnal

temperature gradient (Gregory 2000). The close align-

ment between biogeochemical tracer isosurfaces and


isopycnals results from the combined effects of (i) the

action of the biological pump, which tends to stratify the

biogeochemical tracer concentrations, and (ii) the circu-

lation, which, as it tilts isopycnals in the Southern Ocean,

tilts the biogeochemical tracer surfaces as well. Hence, in

the ocean interior, the weak along-isopycnal gradients of

biogeochemical tracers may reflect the importance of

circulation over local sources and sinks.

3) SCALING OF EDDY-DIFFUSIVE TRANSPORT

Considering the close alignment between bio-

geochemical tracer isosurfaces and isopycnals, an

additional diagnostic is needed to investigate further

the eddy-diffusive transport. A rough scaling of eddy-

diffusive transport for tracers xC across the front and

on an isopycnal layer can be computed as follows

(e.g., Griffies 2004, his section 6.11):

xC52r

0kh(=C) � n dl , (2)

where k . 0 is a coefficient of along-isopycnal eddydiffusivity, h is the isopycnal thickness, C is the tracer

concentration, dl is the front segment, n is the vector

normal to dl, and the overbar denotes a 20-yr average

over a given month. However, given the simple approach

of Eq. (2), we cannot accurately infer the eddy tracer ad-

vective transport by subtracting xC from the eddy com-

ponent shown in Fig. 8. Rather, this scaling allows us to

examine the sign and strength of the along-isopycnal tracer

gradients as a contributor to the eddy-diffusive transport

and to compare the magnitude of eddy-diffusive transport

estimates between the various tracers.

The tracer gradient contribution to the eddy-diffusive

transport is shown in Figs. 10a2–d2. Along-isopycnal

tracer gradients across the PF are integrated along the

PF andwithin isopycnal layers andmultiplied by21 [seeEq. (2)]. Thus, the sign of the eddy-diffusive transport

can also be examined. The eddy-diffusive transport is

southward in all layers for temperature (Fig. 10a2),

while being mainly southward for DIC and northward

for O2 (Figs. 10b2,d2). Eddy-diffusive transport for PO4switches from southward between around 35.7 and

36.6 kgm23 to northward between around 36.5 and

36.9 kgm23 (Fig. 10c2). The double peak in the north-

ward eddy-diffusive transport for PO4 corresponds to

locations of the local PO4 extrema that characterize the

UCDW and LCDW. We also note that, for all tracers,

the profiles show a peak just below the base of the

Ekman layer, indicating that the along-isopycnal tracer

gradients are intense at that depth. The presence of this

intense along-isopycnal tracer gradient suggests seasonal

outcropping of the isopycnals ;36.3 to 36.6 kgm23

south of the PF. Winter isopycnal outcropping leads to

ocean heat loss, O2 ingassing, and CO2 outgassing at the

surface (not shown), as upwelled deep waters are rela-

tively warm, rich in natural DIC, and poor in dissolved

oxygen relative to the preindustrial atmosphere (e.g.,

Dong et al. 2007; Gruber et al. 2009; Garcia and Keeling

2001). Isopycnal outcropping also exposes waters to the

euphotic zone, leading toDICandPO4 drawdown andO2production through photosynthesis. Along the seasonally

outcropping isopycnals, we would thus expect a north-

ward gradient of temperature, DIC, and PO4 and a

southward gradient of O2. These gradients would lead

to a southward eddy-diffusive transport of tempera-

ture, DIC, and PO4 and a northward diffusive transport

of O2; these features are visible in Figs. 10a–d2. Further

support for this explanation comes from the distribution

of an age tracer binned in (SSH; s2) space, which shows

an intensified along-isopycnal gradient across the PF

within this density range, indicating that these iso-

pycnals are ventilated (i.e., in contact with the mixed

layer over a seasonal cycle) south of the PF (not

shown). Moreover, the seasonality of the eddy-

diffusive transport reveals that the magnitude of the

transport peaks in winter within this density range (not

shown), supporting the idea of a winter outcropping of

the isopycnals south of the PF which ventilates the

ocean interior.

We now present a comparison of the magnitude of

eddy-diffusive transport between the tracers in Fig. 10e.

To do so, along-isopycnal tracer gradients are integrated

along the PF and within its core layers and then divided

by the corresponding time-mean component (blue bars

in Figs. 8a2–a5). These gradients are scaled to an eddy-

diffusive transport [xC; Eq. (2)] using a k of 500m2 s21

that corresponds to the best agreement when estimating

latitudinal profiles of xtemp from Eq. (2) and from Lee

et al.’s (2007) method. This value of k lies at the low end

of observational and theoretical values of 500 to

2000m2 s21 for the Southern Ocean (e.g., Ferrari and

Nikurashin 2010; Abernathey et al. 2010; LaCasce et al.

2014). We note that k is expected to vary in space and

time because of mean flow suppression (e.g., Ferrari and

Nikurashin 2010). However, these variations are con-

sistent across all tracers. By ignoring variations in k, we

are thus highlighting the dependence of eddy-diffusive

transport on along-isopycnal tracer gradients and

providing a comparison between different tracers.

Across the PF core, the eddy-diffusive transport for

temperature andO2 is of the same order of magnitude as

the corresponding time-mean component (Fig. 8a, blue

bars), while eddy-diffusive transport for DIC and PO4 is

much weaker (less than 5% of the time mean). This

difference in intensity is because isopycnal gradients of

DIC and PO4 are very weak, unlike those of


temperature and O2 (see Figs. 10a1–d1). To address

potential ambiguity associated with the temperature

scale, the diagnostic was also tested using temperature

anomalies instead of absolute temperature. Using the

time- and space-averaged temperature within the PF

core, or the minimum temperature within the PF core,

as a reference temperature does not affect the conclu-

sion. Eddy-diffusive transport of temperature thus may

play an important role in the cross-frontal heat trans-

port, reinforcing the eddy-advective component by

fluxing heat southward, as demonstrated in previous

studies (Gregory 2000; Lee et al. 2007; Morrison et al.

2013; Griffies et al. 2015). Eddy-diffusive transport of O2may also play an important role in the cross-frontal O2transport but opposes the eddy-advective component

and thus reduces the total southward transport by

FIG. 10. 1) Tracers binned into SSH and s2 coordinates (colors) with solid black contours corresponding to the

tracer isosurfaces. 2) Contribution of along-isopycnal tracer gradients to eddy-diffusive tracer transport across the

PF [2Þh(=C) � n dl; see Eq. (2)]. Vertical profiles have been normalized by their respective maximum absolute

value. Positive values correspond to a northward eddy-diffusive transport. Dashed horizontal linesmark the base of

the Ekman layer (s2 5 36.4 kgm23) and solid horizontal lines the lower extension of the PF core (s2 5

36.9 kgm23). Details of how the limits of the PF core and the Ekman layer are chosen are provided in section 2d.

1) White vertical dotted lines indicate the SSH contour corresponding to the position of the PF (20.95m). Resultsare presented for (a) temperature, (b) DIC, (c) PO4, and (d)O2. (e) Eddy-diffusive transport across the PF [Eq. (2)]

summed over the PF core (s2# 36.9 kgm23) and normalized by the time-mean component (blue bars in Fig. 8a) for

all four tracers.


eddies. Conversely, both DIC and PO4 eddy transports

are dominated by the advective component with little

contribution from eddy-diffusive transport. The differ-

ing contributions of eddy-diffusive components to the

eddy transports of the four tracers play a role in the

differing contributions of eddy transport to the total

transport that we see in Fig. 8a. However, eddy-diffusive

transports for biogeochemical tracers are small enough

so that the ratio of the eddy to the time-mean compo-

nents remain very similar to that of mass.

This qualitative assessment of the direction and in-

tensity of tracer eddy-diffusive transport suggests that

eddy-diffusive transport may provide a significant con-

tribution to the southward eddy heat transport due to

strong along-isopycnal temperature gradients.

4. Discussion

a. Relative contributions of eddy-advective andeddy-diffusive transports

The respective role and relative importance of the two

processes by which mesoscale eddies transport tracers,

namely, eddy-advective and eddy-diffusive transports,

are topics of active debate. While estimating each com-

ponent from observations remains a challenge (Palter

et al. 2013), it has recently become possible in models

with the advent of eddying climate models. Comparing

the eddy-induced cross-frontal transports of heat, DIC,

PO4, and O2 and estimating their eddy-diffusive compo-

nent, we find that eddy-advective transport is likely to

be a leading-order component for all four tracers. Results

for PO4 are in line with the study of Lee and Williams

(2000), which demonstrated that the advective compo-

nent dominates over the diffusive component for long-

lived nutrients. In the Southern Ocean, the biological

pump has a relatively low efficiency due to limited

availability of light andmicronutrients, so that PO4 can be

considered a long-lived nutrient. Eddy-diffusive trans-

port of heat is found to be important for eddy heat

transport across the PF core, as isopycnal cross-frontal

temperature gradients are strong over most layers of the

PF core. Using 5-day-averaged output from a high-

resolution model, Lee et al. (2007) computed meridio-

nal eddy-advective and eddy-diffusive transports for heat

across constant latitudes of the Southern Ocean and

found the latter to be around half the magnitude of the

former, a result that is consistent with ours.

However, estimates of eddy-induced diffusive trans-

port from Eq. (2) cannot provide accurate quantifica-

tions to conclude which of the two components of eddy

heat transport is predominant or the importance of the

eddy-diffusive component for the cross-frontal transport

of biogeochemical tracers. We identify here three main

uncertainties in the estimate of eddy-diffusive transport:

First, there is a broad range of values for the eddy-

diffusivity coefficient k that has been estimated from

observations or calculated in models. Second, observa-

tions, theories, and models have all reported enhanced

eddy diffusivities at the steering levels, that is, along the

flanks of the jet and beneath its core (e.g., Abernathey

et al. 2010; Ferrari and Nikurashin 2010; Naveira

Garabato et al. 2011). In this study, we used a constant

k in space and time, which does not account for the

typical enhanced values at the steering levels and at to-

pographic obstacles. Third, while in the nearly adiabatic

interior of the ocean, eddies stir tracers along isopycnals;

in the surface diabatic ocean, they tend to stir tracers

horizontally (Treguier et al. 1997; Ferrari et al. 2008).

The surface diabatic layer mostly corresponds to the

mixed layer, with an average depth around 100m along

the PF in themodel and thus lies within theEkman layer.

In this study, we only investigated the tracer-diffusive

transport from along-isopycnal tracer gradients, such

that a part of the eddy-diffusive transport has been

overlooked. Neglecting the horizontal eddy-diffusive

transport might explain why the eddy-diffusive trans-

port remains so low in layers lighter than 36.1 kgm23 in

our diagnostics (Figs. 10a2–d2). However, from the

tracer distributions at the surface, we can infer that, in

the mixed layer, eddies would diffuse heat southward,

hence reinforcing the eddy heat advection, and diffuse

biogeochemical tracers northward, hence opposing the

eddy advection component. This inference still supports

the results showing that eddy tracer advection is a

leading-order component of the tracer transport across

the PF core.

b. Comparison between the Polar Front and theSubantarctic Front

Another important front of the Southern Ocean is the

SAF, which delimits the northern boundary of the ACC

and sits between the subduction sites of AAIW and

SAMW. This study presents results for the PF, the first

front that upwelled heat, carbon, oxygen, and nutrients

encounter on their route to lower latitudes. We also

analyzed transport across the SAF and now summarize

those results in comparison to the PF (Fig. 11).

Transport features across the PF discussed herein are

also found to generally hold for the SAF, with an en-

hancement of tracer transport where the SAF encoun-

ters major topographic obstacles due both to an

intensification of the eddy activity and misalignment of

the mean flow with the path of the front. As for the PF,

transport across the SAF core is largely dominated by

the northward Ekman contribution. However, there is


no eddy-prevailing regime below the Ekman layer but

rather a combined contribution from eddies and geo-

strophic time-mean transport. As a result, the eddy ef-

fect on the total tracer transport across the SAF is

weaker than across the PF, and a larger part of the

southward transport is supported by geostrophic time-

mean transport including near-topographic obstacles.

Eddy-advective transport dominates eddy tracer

transport across the SAF core with two notable ex-

ceptions (Fig. 11). Eddy-diffusive transport for PO4

contributes a significant northward transport across

the SAF that generally reinforces eddy-advective

transport below the Ekman layer. As a result, PO4 is

the only tracer showing a net northward eddy trans-

port across the SAF core. Eddy-diffusive transport

for heat may dominate over the advective component

below the Ekman layer, hence strongly reinforcing

the southward geostrophic transport across the SAF

core. However, eddy-diffusive transport for heat is

generally weaker across the SAF than across the PF,

FIG. 11. Schematic of mass and tracer transport across the core of the PF and the SAF in regions of topographic

obstacles and flat-bottom ocean. Our study considers ocean interior transport down to the bottom of the jet core

(;2000m). Straight arrows indicate the mass and advective tracer transports decomposed into time-mean com-ponent (blue) and eddy-advective component (red). Wavy arrows indicate the along-isopycnal eddy-diffusive

transport for temperature (light blue), DIC (magenta), PO4 (green), and O2 (yellow). The size of the arrows scales

qualitatively with the importance of the processes for total transport at each front, with a missing arrow meaning

that the process was found to have a negligible contribution to the total transport. Note that wavy arrows (i) are not

on the same scale as straight arrows, as time-mean transport is found to be generally much stronger than eddy-

diffusive transport for tracers (see section 3b), and (ii) show the alongfront-averaged eddy-diffusive transport for

tracers, as differences between eddy tracer–diffusive transport in regions of topographic obstacles and flat-bottom

ocean have not been investigated in this study.


as isotherms tend to be more aligned with isopycnals

at lower latitudes. The SAF is indeed known to mark a

transition in the balance of stratification in the

Southern Ocean from temperature and salinity

equally contributing to stratification south of the SAF

to a temperature-dominated stratification north of

the SAF (Pollard et al. 2002). Overall, the role of

eddy-diffusive transport for biogeochemical tracers is

more important across the SAF core than across the

PF core, due both to the role of eddy-advective

transport being weaker and isopycnal tracer gradi-

ents being stronger at the SAF (in particular for DIC

and PO4).

5. Summary

This study uses an eddy-rich climate model coupled

to a simplified biogeochemical model to examine the

processes driving the transport of heat, carbon, oxygen,

and nutrients (phosphate) across the Polar Front (PF)

and above the sill of major topographic obstacles, a re-

gion referred to as the PF core. We focus on the role of

mesoscale eddies relative to other processes, in partic-

ular the Ekman transport whose role has received much

attention so far. We find the following:

d Mesoscale eddies transport tracers southward across

the PF core. In the Ekman layer, southward eddy

transport partially compensates the intense north-

ward Ekman transport, which is the main driver of

tracer transport across the PF core. Below the Ekman

layer, southward eddy transport dominates the total

transport, hence supporting the transport of tracers

to the Antarctic Divergence. However, most of the

southward branch of the upper cell of the meridional

overturning is found to be achieved by geostrophic

currents that lie below the PF core.d Eddy transport is mostly localized at and near

major topographic obstacles. At major topographic

obstacles, eddies dominate the total transport across

the PF core. Hence, hotspots are found to be privi-

leged pathways for water and tracers toward high

latitudes.d Eddy-advective transport is the leading-order compo-

nent of eddy transport for heat and biogeochemical

tracers across the PF core. Eddy-diffusive transport

may significantly reinforce eddy-advective transport

for heat because of intense northward along-isopycnal

temperature gradients across the PF core. In contrast,

eddy-diffusive transport for biogeochemical tracers is

either small, because of weak along-isopycnal bio-

geochemical tracer gradients, or opposes the eddy-

advective component.

Acknowledgments. The CM2.6–miniBLING control

simulation was run at GFDL through a large co-

operative effort involving a substantial commitment of

computational resources and data storage. C. O.Dufour

was supported by the National Aeronautics and Space

Administration (NASA) under Award NNX14AL40G

and by the Princeton Environmental Institute Grand

Challenge initiative. G. F. de Souzawas supported by the

Swiss National Science Foundation (SNSF) Postdoctoral

Fellowship P300P2-147747 and NASA under Award

NNX14AL40G. A. K. Morrison was supported by the

U.S. Department ofEnergy underAwardDE-SC0012457.

I. Frenger was supported by the SNSF Early Postdoc

Mobility Fellowship P2EZP2-152133. J. L. Sarmiento

was supported by the Southern Ocean Carbon and

Climate Observations and Modeling (SOCCOM)

project under the National Science Foundation Award

PLR-1425989. R. D. Slater was supported by NASA

under Award NNX14AL40G. We thank Michael

Winton, Alison Gray, and Robert Hallberg for helpful

comments and discussions on this manuscript and

Youngrak Cho for his technical help on the schematic

of Fig. 11. We are very grateful to Andrew Thompson

for providing sound and insightful comments through

several rounds of reviews that greatly improved this

manuscript. We also thank an anonymous reviewer for

useful comments.

APPENDIX A

Computation of Cross-Frontal Mass and TracerTransport

a. Kinematics of cross-frontal transport

Let us define a generalized meridional coordinate:

s(x, y, t)5 y2f(x, t) , (A1)

where f(x, t) measures the meridional position of the

front (i.e., a SSH contour that we assume monotonic

with latitude) as a function of zonal position and time.

The volume transport crossing the front is proportional

to the diasurface velocity component [e.g., see section

6.7 of Griffies (2004)], which is given by

V 5ds

dt5

d(y2f)

dt5 y2 (›

t1u›

x)f , (A2)

The diasurface velocity is composed of three c

role of mesoscale eddies in cross-frontal transport of heat ......ekman layer, the southward eddy...

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